Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - Guided Practice for Example 4 - Page 531: 7

$y=0.277x^2.09$

Let $y=ax^b$. Then our equations are: $8=a5^b$ and $34=a10^b$. If we divide the second equation by the first one we get: $4.25=2^b$. Then: $b=\ln_2{4.25}\approx2.09$. Then $8=a5^{2.09}\\a=\frac{8}{5^{2.09}}\\a\approx0.277$ Thus $y=0.277x^{2.09}$